docs: improve contributor onboarding and setup instructions (#718)

## Summary

This PR improves the contributor onboarding documentation by adding
missing setup details and correcting example instructions.

## Changes

- Added Docker Desktop prerequisite information for running integration
tests
- Added guidance for verifying Docker is running before executing
`pytest`
- Added Deepgram API key setup instructions required for running
examples
- Added Windows-specific Poetry PATH troubleshooting guidance
- Corrected example execution instructions to match the current
repository structure
- Added verification steps and expected outputs to help contributors
validate their setup

## Motivation

While following the contribution guide, I encountered several setup
issues that were not documented:

- `poetry` command not recognized due to PATH configuration
- Integration tests failing when Docker Desktop was not running
- Missing instructions for obtaining and configuring a Deepgram API key
- Example command referencing an outdated/non-existent file path

These updates aim to make the onboarding process smoother and reduce
setup friction for new contributors.

## Testing

- Successfully installed dependencies using Poetry
- Successfully ran test suite (`199 passed, 4 skipped`)
- Successfully executed the transcription example after configuring the
required API key